4. Building a 2-D Model for the IPT

To construct a two-dimensional model of the density and temperature in the torus, the 9 different particle species yield 9 equations of the form (10) which, completed with the equation of charge neutrality, permit us to calculate the normalized density profiles along the magnetic field $n(s)/n(0)$. The normalized temperature profiles $T_{\parallel,\perp}(s)/T_{\parallel,\perp}(0)$ are then obtained using the 9 corresponding equations of the form (11) or (12). Details of the calculation are given in the appendix.

Since the model has two dimensions, we may distinguish between input parameters concerning the radial dependency (namely the equatorial density $n(0)$ and temperatures $T_{\parallel}(0)$, $T_{\perp}(0)$ at a given Jovicentric distance) and those concerning the latitudinal dependency of the model (namely $n(s)$ and $T_{\parallel,\perp}(s)$ at an altitude $s$ from the centrifugal equator) which both depend on the magnetic field geometry and on the bi-kappa distribution parameters $A_0$ and $\kappa$.